Show that the area of the triangle contained between the vectors veca and vecb is one half of the magnitude of vecaxxvecb.

Show that the area of the triangle contained between the vectors veca

1.	Show that the area of the triangle contained between the vectors veca and vecb is one half of the magnitude of vecaxxvecb.
Answer» Solution :In `DeltaOAB, vec(OA)=VECB, vec(OB)=veca` and `angleAOB=theta and AC=h` `:.` from `DeltaACO` `(AC)/(OA)=SINTHETA` `:. H=bsintheta` Now AREA of `DeltaOAB=(1)/(2)xx\|vec(OB)\|h` `=(1)/(2)\|veca\|h` `:.` Area = `(1)/(2)absintheta [because h=bsintheta]` `=(1)/(2)\|veca\|\|vecb\|sinthetahatn` `:.vecS=(1)/(2)(vecaxxvecb)hatn` Magnitude `S=(1)/(2)\|vecaxxvecb\|`